Prime numbers is one of kind number that have many uses, one of which is cryptography. The uniqueness of prime numbers in their divisors and distributions causes prime numbers to be widely used in digital security systems. In number theory, one of famous theorem is Euclid theorem. Euclid theorem says about infinitely of prime numbers. Many alternative proof has been given by mathematician to find new theory or approximation of prime properties.  The construction of proof give new idea about properties of prime number. So, in this study, we will give an alternative proof of Euclid theorem and investigate the properties of prime in distribution.